At a lunar research base, Emek and Tara prepared to connect three new laboratory modules to the power system. Before activating them, they had to confirm that the expanded solar array could meet their energy needs. The control display represented the array's available power by (2^7)(2^5)/(2^4) kilowatts. Emek combined the powers in the numerator to get 2^12, then used the quotient rule to simplify the expression to 2^8, or 256 kilowatts. The existing base required 2^6 kilowatts, and the three new modules together required another 2^7 kilowatts. Tara calculated 64 + 128 = 192 kilowatts for the total requirement. She then compared 192 kilowatts with the array's 256-kilowatt output. The difference was 64 kilowatts, giving the base extra capacity for unexpected demand. After checking each exponent calculation, Emek and Tara confirmed that the solar array could safely power all the connected modules and approved the expansion.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
When multiplying powers with the same base, add the exponents. When dividing, subtract the exponent in the denominator.
Which expression correctly shows how Emek can simplify the solar array's available power, (2^7)(2^5)/(2^4)?
2^(7 + 5 + 4) = 2^162^(7 - 5 + 4) = 2^62^(7 + 5 - 4) = 2^82^(7 - 5 - 4) = 2^-2
Correct. Adding the numerator exponents and subtracting the denominator exponent gives 2^8.
Not quite. Review how exponents change when powers with the same base are multiplied and divided.
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Hint
Evaluate each power of 2, add the two power requirements, and subtract that total from the array's output.
The solar array provides 2^8 kilowatts. After the base uses 2^6 kilowatts and the three new modules use 2^7 kilowatts, how many kilowatts of capacity remain?
Correct. The solar array has 64 kilowatts of capacity remaining.
Check the values of 2^8, 2^6, and 2^7, then subtract the total requirement from the available power.
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Hint
Start with the 64 kilowatts of extra capacity from the story and evaluate 2^5.
Suppose an additional instrument requiring 2^5 kilowatts is connected after the expansion. Which statement correctly describes the solar array's remaining capacity?
The array would have 16 kilowatts remaining.The array would have 32 kilowatts remaining.The array would have 64 kilowatts remaining.The array would not have enough power.
Correct. The new instrument uses 32 of the 64 extra kilowatts, leaving 32 kilowatts.
Not quite. Evaluate 2^5 and subtract it from the extra capacity available after the expansion.
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Ay Üssüne Enerji Sağlamak
TR
ARC_G09_OPS_02_STORY_01
Ay Üssüne Enerji Sağlamak
Powering the Lunar Base
EN
ARC_G09_OPS_02_STORY_01
Powering the Lunar Base